[tex] - 2 {x}^{2} - x + 10 = 0[/tex]
[tex]a = - 2[/tex]
[tex]b = - 1[/tex]
[tex]c = 10[/tex]
[tex]\Delta = {b}^{2} - 4ac[/tex]
[tex]\Delta = {( - 1)}^{2} - 4 \times ( - 2) \times 10[/tex]
[tex]\Delta = 1 + 80[/tex]
[tex]\Delta = 81 > 0 = > \exists \: x_{1} \: \neq \: x_{2}\in\mathbb{R}[/tex]
[tex]x_{1,2}=\frac{-b\pm\sqrt{\Delta}}{2a}[/tex]
[tex]x_{1,2}=\frac{-( - 1)\pm\sqrt{81}}{2 \times ( - 2)}[/tex]
[tex]x_{1,2}=\frac{1\pm9}{ - 4}[/tex]
[tex]x_{1}=\frac{1 +9}{ - 4}[/tex]
[tex]x_{1}=\frac{10}{ - 4}[/tex]
[tex]x_{1}= - \frac{10}{4}[/tex]
[tex]x_{1}= - \frac{5}{2}[/tex]
[tex]x_{2}= \frac{1 - 9}{ - 4}[/tex]
[tex]x_{2}= \frac{ - 8}{ - 4}[/tex]
[tex]x_{2}= 2[/tex]
[tex] = >A\cap[ \sqrt{3} ,3] = x_{2} = 2[/tex]
